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%-I ati~~i?avi-L&~;u (ST1031 7ui 1 ti.v,, Lodlob

doifnarw? 5 SaJ-z sibi-2________________________________________-------------.----------------------------------

Gauuzuitun;7aou I t&*~"al &"niPl%ud~n'uumaun *ho uil nivyia ,LRaL;ai& LBWI h R'IRDU

i~QrCc3~~q*~(Au~~i nu.&~-r lmufiim&niGon~ x t;,duilnAnu?,~u;lZ~Pli~imuutuuui~iln c GaLr-rndpn

uuaoq~~illl Hi& ,-m1aau 15.00 -1u30 H

____________________------------------------------------- -- -r_-- ------------------------

l ) Pk= L-G!Lf 100 b) Pk= ikn

L-7 yjo-FI I

221

A l

An B

A ” B

A - B

2 2 3

A l

2 2 4

A ?

2 2 5

-1 t';;'= 2.064 b) t25-1=.05 2.060 m) t25-1 --025 2.060 d) t25-1.025= 2.064

2 2 6

Al

2 2 8

Al ST 103

I 1 om-

0.a

.

1dl.vCritfcal Valuer of the I Distribution

-

TabI* VI* Critical Valuer

of the Chi-Square Distribution0 i

l- 1--r

0 . 1 0 0.0s-

0.050.95 0.02: l- D.01

00'393 3.8410.103 5.9910352 7 8150.711 9.4881.145 11.070

6.6359.21011.34513.27715.086

1.635 12 5922.167 14.0672.733 15.5073.325 I6 9193.940 18.307

5.0247.3789.348Il.14312.832

14.449t

16.01317.53519'26481

1681218.4752009021.66623.209

4.5755.2265 8926 5717261

l9675 21.920 24.72521026 23 337 26.21722 162 24.736 27.68823685 26.119 29.14124 996 27.488 30.578

7.962 26296 28.845 32.ooO8612 21587 30.191 33.4099 390 28.869 31.526 34.8050 117 30,144 32 852 36.1910851 31.410 34.170 37.566

I 5912 3383.0913 8484.611

32671 35.479 38 93233 924 36781 40.289l5.172 38.076 41.63836.415 39 364 42.98037.652 40.646 44.314

5 3796.1516.9287.7088.493

IS.885la.113II 337t2.55713.773

41 92343.19444.46145.72246.979 I

45 64246.96348.27849.58850.892

0.01Y 0.005

3.078 6.314 12.706 31.821 63.65718% 2.920 4.303 6.965 9.9251.638 2.353 3.182 4.541 5.8411.533 2.132 2.776 3.747 4.6011.476 2.015 2.571 3.365 4.032

;8910

1.440 1.943 2.447 3.143 3.7071.415 1.895 2365 2.998 3.499I.397 1.240 2.306 7-w 3.3551.383 1.833 2.262 2.821 3.2501.372 1.812 228 2.764 3.169

II 1.363 1.7% 2.201 2.718 3.10612 1.356 1.781 2.179 2.681 3.05513 1.350 1.771 2.160 2.650 3.01214 1.345 I.761 2.145 2.624 2.97715 I.341 1.753 2.131 2.602 2.947

I6171g

z

1.337 1.746 2.120 2.583 2.9211.333 1.740 2.110 2.567 2.8981.330 1.734 2.101 2.552 2.8781.328 1.729 2.093 2.539 2.8611.325 1.725 2.086 2.528 2.845

212223l425

2627

iiid.

1.323 1.721 2.080 2.518 2.8311.321 1.717 2.074 2.508 2.819I.319 1.714 2.o69 2.5w 2.8071.318 I.711 2.o64 2.492 2.797I.316 1.708 2.o6o 2.485 2.787

1.3151.314I.3131.3111.2w.

1.7061.7031.7011.6991.645

2.056 2.479 2,7792.052 2.473 2.7712.048 2.467 2.7632.045 2.462 2.756I.960 2.326 2.576

0.995 0.99

0 . 0 ’ 1 5 10 . 0 2 0 101150 2 9 10.554

0.872I.239I6462.0882 558

3.0533.5714.1074.6605.229

5 8126.4087.0157.6338260

P.8979.5423.1963.856,524

2.1982.8793.5651.2561.953

i.9i5-_

0.0'9820.05060.2160.484

O.B.35

7 879IO.59712.8381486016.7Y)

18.548iO.i7621.95523.58925.188

2675728 30029 81931.31932.801

34.26735.71837.15638 58239.997

41 40142 79644 18145 55846928

48.29049.MJ5099352.33653.672

Y

0.0'390.0100O.Oil70.2070.412

6 0.6767 0.9898 1.3449 ,735IO 2.156

III:I!I4I5

2.6033 0743.5654.0754.601

I6 5.14217 5 697I8 6.265I9 6.84420 7.434

21 8.03422 8.64323 9.26024 9.88625 10.520

2627

:;30

,I 16otl.8oa1246113.121I3 787- -

0.831

I.237I.6902.1802.700$247

3.8164.40450095.6296.262

6.90875648.23189079.591

32830.9821 68924013 120

38444.5735 3086.O476791

nsru~wi~l--_il~sl1~3----_--___----------_-__

il4&mJ----?_YY'~_252_3 9 00-11 30- - - - - - - OAl--L----'-----U.

RnlW~aaU----- -------- --------------

231

6.

10.

11.

12.

13.

14.

15.

16.

18.

19.

20.

21.

2 3 3

22.

23.

7.4.

27.

28.

29.

30.

2 3 4

31.

32.

33.

34.

35,

36,

37.

38.

39.

f d“,luqu x f d fd2 f arm

130 - 140 135 3 -2 -6 12 3140 - 150 145 7 - 1 -7 7 IO150 - 160 155 1 0 0 b 6 ;o1 6 0 - 1 7 0 165 9 1 9 9 29170 - 180 175 7 2 14 28180 1 9 0

36- 18S 4 3 12 36 4 0

40 22 92

l ) p.&-ikn

L - 7�iiTD

“) Pk- L+[ 1g- F

b) Pk’ L-i &-F[ I

d) Pk-i kn

L +7 mJ-pI 1

LO.

41.

12.

13.

44.

45.

46.

41.

48.

49.

50.

51.

52.

l ) 4% x 4’2 b, 5? x 5% -) 5% x 5C7 ‘) 52’3 %,Zc2

2 3 6

5 6 .

5 7 .

5 8 .

5 9 .

6 0 .

6 1 .

6 2 .

6 3 .

6 4 .

x f(x) x.f(x) x2 x2fW

0 4120 0 0 01 a/20 a/20 1 81202 6120 12120 4 241203 2120 6120 9 18/20

26120 50120

n;lwJ7 mju x fJnl¶u~n~ouuwn?u?u P(J+X) srniunil&mqmo

l ) nCx Px(l-PJ"-x ID) ncx P”-x m) nCx (l-PJ"-x c) n'2x (l-PJx

2 3 7

65 .

fib.

67.

68 .

69 .

70.

71.

72 .

73.

74 .

75 .

77.

2 3 8

70.

7 9 .

80.

8 1 .

82.

8 3 .

84.

85.

86.

07.

89.

90.

91.

92.

9 3 .

94.

95.

% .

97.

98.

99.

100.

101.

10 2;

2 4 0

1 0 3 .

104.

10s.

106.

107,

108.

109.

110.

111.

112.

2 4 1

120.

242

om-

0.D)-

Table W* Critical Values

of the Chi-Square Distribution0 x2

lab* v*Critid Valuer of the t Distribution

--I--LI

D.99 0.975 0.95-

0.05 0.025-%A:D.1150.2970.554

1:::Z20.2160.4840.83i

- - - -0.0’39: 3.8410.103 5.9910.352 7.8150.711 $.4881.14s 1 I.070

5 024 6.635 7 879? 378 9.210 10.5979 348 Il.345 12.838

Il.143 13.277 14.86012.832 15.086 !4.750

0.872 1.237 1.635 12.592 14.449 16.812 18.WI.239 I .69U 2.167 14.067 16.013 l a . 4 7 5 20.2781.646 2.180 2.733 15.507 17.531, 20.09Q 21 9352.088 2.700 3.325 16.919 ‘5m3 21 666 23.5892.5511 9247 3.940 IS.)07 20.483 23.2m 25.188

3.053 3816 4.575 19.675 21.920 24.725 26 7573.5il 4404 5.226 21.026 23.337 26.217 28.3004 I07 5009 5.892 12.362 24.736 27.688 29 8194660 5.629 6.571 23 685 26.119 29.141 31.3195.229 6.262 7 261 24.996 27.488 30.578 32.801

5.812 6.908 7.962 2b 296 28.845 32 .m 34.2676.408 7564 8 672 27 587 30.191 33.409 35 7187.015 8.231 9.390 28.869 31.526 34.@05 37.1567.633 8.907 /IO.117 30144 32 852 36.191 38.582a260 9 591 /IO.851 31.410 34.170 37 566 39.997

8.697 10.283 III.591 32.671 35.479 38.932 41.4019.542 10.982 12.338 33.924 36.781 40.289 42.7960.1% Il.689 13.091 35.172 38.076 41.638 44.1810.856 12.401 13.848 36.415 39.364 42.980 45.558I.524 13.120 14.61 I 37.652 40.646 44314 46.928

2.198 13.844 1I,.;79 38.885 41.923 45.642 48.2W2.879 14.573 16.151 40.113 43.194 46.963 49.6453.565 15.308 16.928 41.337 44.461 48.278 50 9934.256 16.047 17.708 42.557 45.722 49.588 52.3364.953 16.791 18.493 43.773 46979 50.891 53.672

1-

Y

l-0.10 0.05

3.078 6.3141.886 2.9201.638 2.353I 533 2.1321.476 2.015

6

:9

10

I . 4 4 0I.4151.3971.y31.372

I . 9 4 3I.8951.8601.8331.812

III2I314I5

l.36jI.356I.350I.345I.341

1.796J ,782I.771I.761I.753

16 I . 3 3 7 1.746I ? 1.333 I . 7 4 0I8 I.330 1.734I9 1.328 1.72920 I.325 1.725

::232425

1.323I.321I.319i.3181.316

1.7211.717I . 7 1 4I.711J ,708

it28

2.-

I.315I . 3 1 41.313I.311I.282

I.7061.703I.7011.6991.645-

-

0.995Y ,

3 t,,,

III

IIIII

0.025 0.01 O.OOS

2.706 31.8214.303 6.9653.182 4.5412.776 3.7472.571 3.365

t53.6579.9255.8414.6044.032

tt :2.m2.2622.228

3.143 3.7072.998 3.4992.896 3.3552.821 3.2502.764 3.169

2.201 2.718 3.1062.179 2.681 3.0552.160 2.650 3.0122.145 2.624 2.9772.131 2.602 2.947

2.im 2.583 2.9212.110 2.567 2.8982.101 2.552 2.8782.093 2.539 2.8612.086 2.528 2.845

2.080 2.518 2.8312.074 2.508 2.8192.%9 2 . m 2.8072.064 2.492 2.7972.cw 2.485 2.787

2.056 2.479 2.7792.052 2.473 2.7712.M8 2.467 2.7632.045 2.462 2.756I.%0 2.326 2.376 - -

OP390.01000.0il70.207

6 0.6767 0.9898 I.3449 I.735

IO 2.156

II 2.603I,? 3.074I3 3.56514 4.075I5 4.601

I6 5.142I7 5 697I8 6 265I9 6.64420 7.434

21 8.0342l 8.64323 9.260-24 9.88625 IO sm

26

i.i2930

II.160lIx%12.46113.12113.787

-

Ntbco

nsrux4%1 --amLc.3--- _--_-___-____--_-__-_ --

~w&,ou-~4~W"~ 2523--c----.e----- ,,a, --%Qo,_lLJ_o--- u.

aO,W~RO"---_--_---___- -____-___-_-_

1 .

2 .

3 .

4.

5 .

6 .

7.

8.

9 .

2 4 6

10 - 15 12.5 1 -2 -2 4 115 - 20 17.5 2 - 1 -2 2 320 - 25 22.5 3 0 0 0 625 - 30 27.5 2 1 2 2 830 - 35 32.5 1 2 2 4 935 - 40 37.5 1 3 3 9 10

16. .) X= a - iZfd

b) xx i Xfd

z- Zf-)

23.

24.

25'.

26.

27.

28.

2 4 7

“lW?p x1 3 0 - 1 4 0 1 3 51 4 0 - 1 5 0 1451 5 0 - 1 6 0 1 5 51 6 0 - 1 7 0 1651 7 0 - 1 8 0 115180 - 1 9 0 185

f d fd fd2 f ETraII

3 -2 -4 1 2 37 - 1 - 7 7 1 0

1 0 0 0 0 2 09 1 9 9 2 97 2 1 4 2 8 3 64 3 1 2 3 6 40

40 2 2 9 2

Rl~l\1L,9~,,9UR7,Ud~lilU;iwff"WilwPPllnaneh ti%?Jansu InTlhtininwBn in &iillti- 2

IhYn x f f x (X-XI f Ix-XI ( x - x ) f (x-a2

3 5 - 45 40 3 1 2 0 20 60 400 1 2 0 04 5 5 5 50 5 2 5 0 1 0 50 1 0 0 500-5 5 - 6 5 60 5 300 0 0 0 06 5 - 1 5 7 0 4 280 1 0 40 100 4007 5 - 8 5 8 0 2 1 6 0 2 0 4 0 400 800a 5 - 9 5 9 0 1 9 0 3 0 3 0 900 900

2 0 1 2 0 0 2 2 0 3 8 0 0

2 4 8

“) 0.3

n) O.d

2 5 1

7 0 .

7 1 .

7 2 .

7 3 .

7 4 .

76.

78.

2 5 3

3 6 .

9 7 .

98.

9 9 .

100.

101.

102.

103.

104.

105.

106.

107.

(08.

2 5 4

109.

110.

111,

112.

113.

114.

115.

116.

2 5 5

nzwu?ain. (Xl 91 lllUU7?Jl7l. (Y) x2 Y2 xy

1 2 1 4 22 4 4 1 6 84 5 16 2 5 205 7 2 5 49 3 55 8 2 5 64 40

1 7 2 6 71 158 1 0 5

.

Table V’Crtticat Valves of the 1 Distribution

Table VP Critical Valuesof the Chi-Square Distribution L!2!hB&

(1

0 ri

T

Y

3 .0781 8861.63815331.476

6 1.44G7 1.4138 1 .3979 1 .383

1 0 1 3i2

II \ 36j1 2 I 35613 I.3501 4 I 3451 5 I 141

16 I 3371 7 1 33318 1 33019 I 12s20 , 325

21222 32.425

2 62 7282 9nf.

1315I314I .313,311I.282

6.314 12.7062.920 4.3032 .353 3 .1822 .132 2 .7762 .015 2 .571

31.8216 .9654 .541

xi

63.6579 9255.8414 .6044 .032

-

I2345

FT

0 .0 ’39O.OlMO.Oil;0 .2070 .412

I.943 2.447 3.143 3 .707I 895 2.365 2 998 3 .499I .860 2.306 28% 3 .355I.833 2 262 2 .821 3 .2501.812 2 .228 2.764 3 169

6 0.6767 0.9898 1 .3449 I.73510 2 156

1 7 % 2 201 2718 3 to6 II 2 .603I.782 2.179 2 681 3 .055 12 3 .074I 771 2 .160 2 650 3 012 1 3 3 .5651 .761 2 .145 2 624 2 977 1 4 4 .075I.753 2 131 2 602 2.94, 1 5 4.601

I 746 1 I20 2 583 2921I 740 2 110 2 567 2 898I 734 2 101 ? 552 2 878I 729 2OY3 2 539 2 8611 .725 2 086 1528 2 845

1 6 5 14217 5 69713 6 2651 9 68442 0 7 414

,721,117,714,711

I 708

2 “X02 074: 0602 “fJ2 06”

2 0562 0522Lw2 MSI 960

2 518 2 8312 508 2 5192500 2 no72 492 2 7Y72 485 2.787

I.706I JO,I701I 699I 645

2 479 2 7792 .473 2 77,2 467 2 .7632 462 2 .7562 .326 2.576

262 72 8293 0 i

II l&2I, ,808I2 46113.12113.787

0 .025 0.01 0.005

1-

Y

-

0.995 0 .99

0.0’150.02010.1150 .2970 .554

0 872I 239I .&62.0882 558

3 .0533 .5714 10746605.229

5 .8126 .4087 .0157 63382.50

3 8973.5421196) 8561 524

! 198! 879I 565I256I .953

0 .975 0 95 0.05

0 0’98;0.050602160 4.340.831

- -00139.0 10303520.711I.145

3.8415.9917.815$48811.07c

1.237 1.635 12.5921 .690 2.167 14.0672 180 2.733 I5 5072 .700 3.325 16.919047 3.940 18.307

3 .616 4.575 19.6754 .404 5.226 210265.lw9 5.892 22.3625 .629 6.571 236856 .262 7.261 24.996

6.W8 79627 .564 8.6728 .231 9.3908 907 0.1179 591 0.851

26.29627 587X869IO 144I/ 410

0 283 1.5910 982 2 338I 689 3.0912 40, 1.8483 120 4611

1267113924I5 172IhJlSx7652

3 844 5 3794 573 6 I515 .308 6928so47 7 708ii91 8493

8 8850 113I 337? 5573 773

!I1:I:)

0.025

5.0247.3789.34811.14312.832

14.44916.01317.535l&Q232w 463

2192023.33724.:3626 11927.488

28.84530 19131 ‘ 2 632 85234 170

15.47916 78,38 076iv 36410 646

LI Y2313 194kt 461I5 J2216 979

-0.01

6.6359 2icii.34513.27715.086

16.81218.4752009021 66-523 209

24.7252621727 68829.14110.578

"'13;.0289I 0382 9804 314

5 64269638 2789 5830.892

0005- -: 87'!059;I2838148&1675C

18.54820.27821 95523 58925 188

26i5728 3M2981931 31932 801

X26?35 71837 15618 582x.997

II JOI$2 746u 181I5 559Id 928

18 3019.615,0993,? 336i3672-

.~~..~H~~~.**.~**~.,HH~~~H~~~~+H~~~u~~~~~**=H=*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . ..*......*....**.....*......8. 8.. .. .i

ikJtii... ~~~~~~~~~~~~~~~~~~~~~~~~~~ 4’

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Ramkhamhaeng University Press. :$.bb w.~~~~~HH~~~~HHH~H~HH*~~~~~~~~~~~~~.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . .

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